Getting Started 
Misconception/Error The student does not know the formula for the volume of a pyramid. 
Examples of Student Work at this Level The student cannot correctly identify a formula for finding the volume of a pyramid. The student writes an incorrect expression and imprecisely describes the meaning of the variables.

Questions Eliciting Thinking What are the parts of a pyramid? If you were to create a net of a pyramid, what twodimensional shapes would you draw?
What is a variable?
What terms describe the dimensions of the pyramid? 
Instructional Implications Ensure that the student is familiar with pyramids and prisms as well as terms used to describe their parts and dimensions such as base, lateral surface, height, and slant height. If necessary, review the possible formulas for finding the area of polygons (that might represent the base of a pyramid) and be sure the student understands how to apply them. Remind the student that the volumes of prisms and cylinders can be found by multiplying the area of their bases by their heights. Similarly, the volume of a pyramid or cone can be found by multiplying the product of the base area and height by onethird. Explain (or use a demonstration to show) why the volume of a pyramid is onethird the volume of a prism with the same base area and height. Emphasize the general formulas for finding the volumes of prisms and pyramids. Explain to the student that the general formulas along with some basic area formulas are all that is needed to calculate volumes of prisms, cylinders, pyramids, and cones.
Provide specific examples of pyramids (include some with square, rectangular, and triangular bases) and ask the student to identify the relevant formulas (the volume formula and the formula for calculating the area of the base) and calculate the volume. Provide feedback. 
Making Progress 
Misconception/Error The student does not understand the variables in the formula. 
Examples of Student Work at this Level The student correctly identifies a formula for finding the volume of a pyramid but:
 Does not specifically explain the meaning of each variable and does not correctly label the diagram.
 Labels slant height but refers to it as the height.
 Does not describe B as the area of the base.

Questions Eliciting Thinking Can you identify any parts of a pyramid? How does the formula you wrote correspond to the diagram?
What is the difference between the base and the area of the base?
How do you measure the height of a pyramid? Is the height on the threedimensional figure? Where is the height? 
Instructional Implications Review the terms used to describe the parts and dimensions of pyramids and prisms such as base, lateral surface, height, slant height. Provide the student with the general formula for finding the volume of a general pyramid, V=Bh clearly identifying the meaning of the variables in the formula. Be sure the student can locate the base and height on a model and in a drawing of a pyramid. Discuss finding an appropriate formula for calculating the area of the base.
Provide specific examples of pyramids (include some with square, rectangular, and triangular bases) and ask the student to identify the relevant formulas (the volume formula and the formula for calculating the area of the base) and calculate the volume. Provide feedback. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student writes:
 V=Bh or V= lwh (for the rectangular pyramid in the diagram).
 V is volume and B is the area of the base; l is length of the base, w is width of the base and h is the height of the pyramid.
 The student correctly labels the variables on the diagram.

Questions Eliciting Thinking Can you explain why there is a factor of in the formula for finding the volume of a pyramid?
Can you explain how the two different volume formulas, V=Bh and V= lwh are related? Why do they result in the same answer? 
Instructional Implications Provide opportunities to solve mathematical and realworld problems by calculating volumes of prisms and pyramids. Include some figures that are composites of these solids.
Consider implementing other MFAS tasks for this standard (8.G.3.9). 